hdu_1710_Binary Tree Traversals(二叉树的重构)

最新推荐文章于 2021-10-05 15:41:21 发布

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本文介绍了一种根据二叉树的前序和中序遍历结果，转换得到后序遍历结果的方法，并提供了一个C++实现示例。通过递归的方式构建二叉树结构，最终输出后序遍历序列。

Description

A binary tree is a finite set of vertices that is either empty or consists of a root r and two disjoint binary trees called the left and right subtrees. There are three most important ways in which the vertices of a binary tree can be systematically traversed or ordered. They are preorder, inorder and postorder. Let T be a binary tree with root r and subtrees T1,T2.

In a preorder traversal of the vertices of T, we visit the root r followed by visiting the vertices of T1 in preorder, then the vertices of T2 in preorder.

In an inorder traversal of the vertices of T, we visit the vertices of T1 in inorder, then the root r, followed by the vertices of T2 in inorder.

In a postorder traversal of the vertices of T, we visit the vertices of T1 in postorder, then the vertices of T2 in postorder and finally we visit r.

Now you are given the preorder sequence and inorder sequence of a certain binary tree. Try to find out its postorder sequence.

Input

The input contains several test cases. The first line of each test case contains a single integer n (1<=n<=1000), the number of vertices of the binary tree. Followed by two lines, respectively indicating the preorder sequence and inorder sequence. You can assume they are always correspond to a exclusive binary tree.

Output

For each test case print a single line specifying the corresponding postorder sequence.

Sample Input

9
1 2 4 7 3 5 8 9 6
4 7 2 1 8 5 9 3 6

Sample Output

7 4 2 8 9 5 6 3 1

根据前序与中序遍历结果输出后序结果。

代码

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

int pre[1005],in[1005];
int post[1005];
int flag;
void CreateTree(int preL,int preR,int inL,int inR)
{
    int i;
    int l;
    int r;
    if(preL <= preR && inL <= inR)
    {
        for(i=inL;i<inR;i++)  //根据中序排列确定左右子树
        {
            if(pre[preL] == in[i])   //前序左边第一个是根节点，在中序以根节点为分界线分为左右子树
                break;
        }
        l = i-inL;  //左子树的个数
        r = inR-i;  //右子树的个数
        if(l > 0)
            CreateTree(preL+1,preL+l,inL,i-1);
        if( r > 0)
            CreateTree(preL+l+1,preR,i+1,inR);


        //printf("%d ",pre[preL]);//后续结果存到前序数组里了
        if(flag == 1)  //用flag 的意义在于格式问题
        {
            printf("%d",pre[preL]);
            flag = 0;
        }
        else
            printf(" %d",pre[preL]);
    }
}
int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        flag = 1;
        for(int i=0;i<n;i++)
            scanf("%d",&pre[i]);
        for(int i=0;i<n;i++)
            scanf("%d",&in[i]);
        CreateTree(0,n-1,0,n-1);
        printf("\n");
    }
}